Because type is (usually) syntactic rather than semantic, i.e. it looks at what the Maple structure of an object is, rather than the mathematical nature of what it represents.  In this case, your expression is not literally an  integer or  a quotient of two integers, so it is not of type rational.  You can, however, use simplify to transform this expression into 2.

It works for me (after correcting a couple of typos):

> plottools[transform]((x,y)->[y,x])(loglogplot([A, B, C, E], z = 0.01 .. 1));

It works for me (after correcting a couple of typos):

> plottools[transform]((x,y)->[y,x])(loglogplot([A, B, C, E], z = 0.01 .. 1));

The VectorCalculus procedures might write a certain quantity (e.g. a path integral) as an ordinary integral.  Once you have that integral you can use Student[Calculus1] procedures to do the integration step-by-step.  Is that what you mean?

The VectorCalculus procedures might write a certain quantity (e.g. a path integral) as an ordinary integral.  Once you have that integral you can use Student[Calculus1] procedures to do the integration step-by-step.  Is that what you mean?

Actually, I'm surprised Maple didn't complain about verdana: the help pages ?plot,options and ?plot3d,options say the only allowed font families are TIMES, COURIER, HELVETICA, and SYMBOL, and values must be in uppercase.  HELVETICA does result in sans-serif fonts, but the 2D and 3D versions are certainly different fonts.
 

Actually, I'm surprised Maple didn't complain about verdana: the help pages ?plot,options and ?plot3d,options say the only allowed font families are TIMES, COURIER, HELVETICA, and SYMBOL, and values must be in uppercase.  HELVETICA does result in sans-serif fonts, but the 2D and 3D versions are certainly different fonts.
 

There is no Classic interface for the Mac.  You can, of course, open a Classic worksheet (.mws file) with the Standard interface.

There is no Classic interface for the Mac.  You can, of course, open a Classic worksheet (.mws file) with the Standard interface.

If I'm not mistaken, an asymptotic expression for this integral as a -> infinity is

sum(2*(4-2^(-2*n))*bernoulli(2*n+2)/(n+1)!*a^(-n-1/2)*Pi^(1/2),n = 0 .. infinity)

I'm afraid Joe's results for 1 and sqrt(Pi) don't stand up to closer scrutiny.  In particular:

> evalf(J2(1)-10/49*7^(3/5)*ln(3)^(3/5)/ln(2)^(3/8),50);

-.158905988728675873382420871174120680348776e-8

> evalf(J2(Pi^(1/2)) - 10/49*7^(3/5)/ln(3)^(8/7)*Zeta(5)^(8/5),50);

-.363480490450459846340365954293864958366955e-8

If I'm not mistaken, an asymptotic expression for this integral as a -> infinity is

sum(2*(4-2^(-2*n))*bernoulli(2*n+2)/(n+1)!*a^(-n-1/2)*Pi^(1/2),n = 0 .. infinity)

I'm afraid Joe's results for 1 and sqrt(Pi) don't stand up to closer scrutiny.  In particular:

> evalf(J2(1)-10/49*7^(3/5)*ln(3)^(3/5)/ln(2)^(3/8),50);

-.158905988728675873382420871174120680348776e-8

> evalf(J2(Pi^(1/2)) - 10/49*7^(3/5)/ln(3)^(8/7)*Zeta(5)^(8/5),50);

-.363480490450459846340365954293864958366955e-8

Basically, dsolve is set up for the "usual" situation where you have existence and uniqueness.  If you want to deal with one of these pathological situations, you must do some careful analysis.  Start with the general solution

> dsolve(diff(x(t),t) = sqrt(x(t)));

x(t)^(1/2)-1/2*t-_C1 = 0

Note that this does not include the singular solution x(t) = 0.  Maple's solution is  defined for t >= - 2 _C1, but can be continued as x(t) = 0 for t < -2 _C1.  In particular this gives solutions satisfying x(0)=0 for any _C1 <= 0.

Basically, dsolve is set up for the "usual" situation where you have existence and uniqueness.  If you want to deal with one of these pathological situations, you must do some careful analysis.  Start with the general solution

> dsolve(diff(x(t),t) = sqrt(x(t)));

x(t)^(1/2)-1/2*t-_C1 = 0

Note that this does not include the singular solution x(t) = 0.  Maple's solution is  defined for t >= - 2 _C1, but can be continued as x(t) = 0 for t < -2 _C1.  In particular this gives solutions satisfying x(0)=0 for any _C1 <= 0.

dsolve is only for ordinary differential equations, not delay-differential equations.

There are various other techniques besides the one I mentioned.  For linear delay-differential equations I'm told the standard reference is R.E. Bellman and K.L. Cooke, "Differential-Difference Equations".  

dsolve is only for ordinary differential equations, not delay-differential equations.

There are various other techniques besides the one I mentioned.  For linear delay-differential equations I'm told the standard reference is R.E. Bellman and K.L. Cooke, "Differential-Difference Equations".